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Sunday, March 27, 2011

The low volatility portfolio recommended for this week is (ticker notation):

'ABT' 'MO''AMGN''BCR''BDX''CVS''CPB''CLX'

'ED''FDO''GIS''HRL''JNJ''K''KMB''LH''MKC'

'MCD''PEP''PG''RAI''SO''WEC'

Although I recommend a portfolio composition every week, it is desirable to maintain this composition for four weeks, and then rebalance with the new composition.

The main difference respect to the last portfolio composition is the purchase of ‘ABT’ and ‘CLX’. The turnover from last month is 17% (due to the portfolio growth in the last month and the purchase of those companies).

Regarding the performance, over the last year (52 weeks), the strategy attained a volatility of 10% (versus 17% of the S&P 500).

The weekly 95%-VaR was 2.4% (versus 4.2% of the S&P 500).

The last year annualized Sharpe ratio of the low vol strategy was 1.36 (after proportional transaction costs of 40 bps were discounted). On the other hand, the SR of the S&P 500 was 0.82 over the same period.

Using a 52-weeks historical method over the last year, the low-vol portfolio attained a higher return (70% of the time) than that of the S&P 500. Moreover, the volatility of the low-vol portfolio was always less than that of the S&P 500.

I have omitted more details regarding the persistence of these conclusions over a longer history because they are roughly the same as those in the previous posts.

As a summary, the low-volatility strategy dominates the market index (70% of the time over the last year), showing it attains consistently better risk-adjusted returns.

The low volatility portfolio recommended for this week is (ticker notation):

'ACS''EBRO''ENG''IDR''ITX''REE''TEF'

Although I recommend a portfolio composition every week, it is desirable to maintain this composition for four weeks, and then rebalance with the new composition.

There is no difference in the portfolio composition respect to that of the last month. For this reason, the turnover from last month is only 2.7% (due to the portfolio growth in the last four weeks).

Regarding the performance, over the last year (52 weeks), the strategy attained a volatility of 18% (versus 28% of the IBEX35).

The weekly 95%-VaR was 4.0% (versus 5.2% of the IBEX35).

The last year annualized Sharpe ratio of the low vol strategy was 0.50 (after proportional transaction costs of 40 bps were discounted). On the other hand, the SR of the IBEX35 was 0.05 over the same period.

Using a 52-weeks historical method over the last year, the low-vol portfolio attained always a higher mean return than that of the IBEX35. Moreover, the volatility of the low-vol portfolio was always less than that of the IBEX35.

I have omitted more details regarding the persistence of these conclusions over a longer history because they are roughly the same as those in the previous posts.

As a summary, the low-volatility strategy dominates the market index (always, and over the last year), showing it attains consistently better risk-adjusted returns.

Sunday, March 20, 2011

The low volatility portfolio recommended for this week is (ticker notation):

'MO''AMGN''BCR''BDX''CVS''CPB''ED''FDO'

'GIS''HRL''JNJ''K''KMB''LH''MKC''MCD'

'PEP''PG''RAI''SO''WEC'

Although I recommend a portfolio composition every week, it is desirable to maintain this composition for four weeks, and then rebalance with the new composition.

The main difference respect to the last portfolio composition is the sale of ‘ABT’. The turnover from last month is 10% (due to the portfolio growth in the last month and the sale of that company).

Regarding the performance, over the last year (52 weeks), the strategy attained a volatility of 10% (versus 16% of the S&P 500).

The weekly 95%-VaR was 2.4% (versus 4.2% of the S&P 500).

The last year annualized Sharpe ratio of the low vol strategy was 1.37 (after proportional transaction costs of 40 bps were discounted). On the other hand, the SR of the S&P 500 was 0.71 over the same period.

Using a 52-weeks historical method over the last year, the low-vol portfolio attained a higher return (70% of the time) than that of the S&P 500. Moreover, the volatility of the low-vol portfolio was always less than that of the S&P 500.

I have omitted more details regarding the persistence of these conclusions over a longer history because they are roughly the same as those in the previous posts.

As a summary, the low-volatility strategy dominates the market index (70% of the time over the last year), showing it attains consistently better risk-adjusted returns.

The low volatility portfolio recommended for this week is (ticker notation):

'ACS''EBRO''ENG''IDR''ITX''REE''TEF'

Although I recommend a portfolio composition every week, it is desirable to maintain this composition for four weeks, and then rebalance with the new composition.

There is no difference in the portfolio composition respect to that of the last month. For this reason, the turnover from last month is only 1% (due to the portfolio growth in the last four weeks).

Regarding the performance, over the last year (52 weeks), the strategy attained a volatility of 17% (versus 28% of the IBEX35).

The weekly 95%-VaR was 4.0% (versus 5.2% of the IBEX35).

The last year annualized Sharpe ratio of the low vol strategy was 0.30 (after proportional transaction costs of 40 bps were discounted). On the other hand, the SR of the IBEX35 was -0.11 over the same period.

Using a 52-weeks historical method over the last year, the low-vol portfolio attained always a higher mean return than that of the IBEX35. Moreover, the volatility of the low-vol portfolio was always less than that of the IBEX35.

I have omitted more details regarding the persistence of these conclusions over a longer history because they are roughly the same as those in the previous posts.

As a summary, the low-volatility strategy dominates the market index (always, and over the last year), showing it attains consistently better risk-adjusted returns.

Wednesday, March 16, 2011

From this post, I will present some of the low-volatility strategies that perform well in practice. I will start with the well-known 1/N policy: simply invest the same amount of money in each of the Nassets considered by the investor.

All the ideas contained in this post are inspired by the following paper (my best wishes to the authors):

There is no better way to start this post than reciting the beginning of the previous paper:

In about the fourth century, Rabbi Issac bar Aha proposed the following rule for asset allocation: “One should always divide his wealth into three parts: a third in land, a third in merchandise, and a third ready to hand.”

Although the 1/N policy, by construction, is not a low volatility strategy, it shares similar properties as the other low volatility strategies. That is, the 1/N portfolio performs better than market indexes in terms of risk and return.

For instance, over the long run the 1/N policy, when applied to the 500 stocks composing the S&P 500 index, attains a bit worse volatility than that of the index but a much better return.That is, it obtains consistently better Sharpe ratios or risk-adjusted returns.

It is true we can obtain a bit better performance if we have the skill to forecast expected returns or if we estimate the associated covariance matrix with state-of-the-art techniques. This is especially true if we use daily or weekly data in our estimations. But the 1/N policy always outperforms the associated market index in terms of risk and return, and this is more than enough for many investors.

The best way to analyze the 1/N performance versus the market one is by looking at the MSCI Equal Weighted Indices. From this information, and over a 10-years period, the world 1/N policy obtained an annual return of 10.9%, versus the 5.7% return of the corresponding world index. That is, it almost doubles the market return. The volatility of the 1/N policy is worse, but only a bit: 14% versus 13.4% for the world index.

In other words, the Sharpe ratio (SR) of the 1/N policy was 0.78 and the SR of the world index was 0.42.

The same results are obtained for other asset compositions: Europe, USA, Japan, etc.

In order to confirm these findings, I have run my own experiments with the stocks composing the S&P 500.

But before, let me add a brief a comment regarding the rebalancing of the 1/N policy. In order to maintain the same weight in each asset, it is necessary to rebalance the portfolio from time to time. This is because the weights of the assets will change due to their price evolution.

But when do we need to rebalance the 1/N policy? Well, it depends on the investor. For instance, the mentioned MSCI equal-weighted indices are rebalanced quarterly. A passive investor may rebalance yearly. In contrast, a more active investor should consider rebalancing on a monthly basis to take advantage of price movements.

I have chosen a monthly frequency to rebalance the 1/N policy. This is the best trade-off I have found between return performance and transaction costs. Later, I will show the results corresponding to a yearly rebalancing frequency (thay are only a bit worse).

The back-test is as follows: at a given week from 2006 up to now, I consider the 1/N policy, and a week later I compute the corresponding portfolio return, net of transaction costs (40 bps) respect to the last portfolio composition. For the S&P 500 index, I consider the corresponding weekly return, but net of any transaction costs.

I repeat this procedure for every week in the last five years obtaining the following performance: portfolio-return mean and volatility, the Sharpe ratio, the Value-at-Risk, and the correlation of the 1/N policy with the market-index return.

As I said, I rebalance the 1/N policy every four weeks in the past. The performance is the following. Over the last five years, the 1/N strategy attained a volatility of 24% (versus 21% of the S&P 500), a 14% worse.

But this is more than compensated by the return performance. The annualized mean return of the 1/N policy (after proportional transaction costs of 40 bps were discounted) was 12% versus the 3.7% return of the S&P 500, more than three times better!

For the 1/N policy, this corresponds to an annualized SR of 0.49. On the other hand, the SR of the S&P 500 was 0.17, almost three times worse.

To have a visual insight of this performance, in the next figure you can see the cumulative returns, over the last 52 weeks, of the 1/N policy (always after transaction costs) and the S&P 500 (no costs).

Note the better performance of the 1/N policy in terms of cumulative returns and the similar levels of risk.It can be observed that always, the 1/N return is higher than that of the S&P 500.

Regarding the rebalance frequency, if we are a more passive investor and want to rebalance only every year, the corresponding results are roughly similar (although a bit worse). For instance, the annualized SR over the last five years of the 1/N strategy was 0.45 versus 0.13 for the S&P 500. That is, we lose 8% in risk-return performance if we rebalance every year instead of every month.

To see if the previous results are consistent over time, next figure shows the rolling excess-return of the 1/N policy respect to the S&P 500. The evolution is from 2006 up to now, and using rolling 52-weeks periods.

It is clear that the 1/N policy outperforms the market index over the last five years. But I prefer to take into account the risk when analyzing the return performance. Hence, next figure shows the evolution for the two portfolios of the annualized SR from 2006, over rolling 52-weeks periods.

We can see that most of the time, the SR of the 1/N strategy is larger than that of the S&P 500.

Finally, in the next graph, we show the evolution of the annualized tracking error of the 1/N policy (respect to the S&P 500) from 2006 up to now.

It can be observed that the mean tracking-error is around 6%, not too low. This allows for better expected returns.

As a conclusion, it is well-established that the 1/N policy dominates the corresponding market indexes, showing it attains consistently better risk-adjusted returns.

To finish this post, I would like to throw up the following question: why do you think the 1/N policy outperforms market indexes in practice?

I do not have a clear answer. But one of the reasons may be the 1/N policy gives more weight to small stocks (compared to cap-weighted benchmarks). But I would like to know your opinions, they will be very welcome.

Edited (April 4th, 2011): Some conclusions from this blog and other forums:

·Equal-weighted indexes put more weight on small and value stocks than cap-weighted index. Hence, as long as these stocks tend to outperform large or growth stocks, equal-weighted indexes will tend to outperform the corresponding market ones.

·Rebalancing frequency may be another reason for the better performance. That is, rebalancing frequency may have a larger impact on equal weights than on cap weights.

The last year annualized Sharpe ratio of the low vol strategy was 1.53 (after proportional transaction costs of 40 bps was discounted). On the other hand, the SR of the S&P 500 was 0.90 over the same period.

Finally, the correlation of the low vol strategy with the S&P 500 along the last 52 weeks was 84%.

Again, all these performance results are consistent over time.

I have omitted more details regarding the performance measures because they are roughly the same as those in the previous posts.

The last year annualized Sharpe ratio of the low vol strategy was 0.41 (after proportional transaction costs of 40 bps was discounted). On the other hand, the SR of the IBEX 35 was -0.07 over the same period.

Note the negative sign in the SR of the IBEX 35, mainly due to the bad performance over the last week.

Finally, the correlation of the low vol strategy with the IBEX 35 along the last 52 weeks was 91%.

Again, all these performance results are consistent over time.

I have omitted more details regarding the performance measures because they are roughly the same as those in the previous posts.

Wednesday, March 9, 2011

This blog is devoted to study the financial performance of low volatility investments, mainly from a statistical point of view. But in this post, I will show some financial explanations to this performance.

Because I am not an expert in Finance, I have collected some good explanations from the financial literature, which can be found at the end of this post. If you have more explanations, I will be very pleased to add them to this post.

Some years ago, I started to study low volatility portfolios from a statistical point of view: In the Markowitz framework, because there is too much estimation error in the expected asset returns, it is desirable to focus only on the variances and correlations of the returns. My surprise was that these portfolios were more efficient (ex-post) than portfolios trying to optimize (ex-ante) the trade-off between risk and return.

Moreover, this good performance is maintained when comparing to broad market indexes. Hence, the performance of low volatility portfolios indicates some type of anomaly in the financial markets. But why does it occur?

Of course, we can say this anomaly occurs because the financial markets are not perfectly efficient all the time. That is, risk and return at the stock level are not highly correlated in practice. Indeed, there exists evidence of stock portfolios that not always exhibit a significant positive correlation between risk and return.

But the question still remains: why do low volatility portfolios perform so well in practice?

I have read several papers and it seems there is no consensus about the origin of this inefficiency. But I show you some of the main explanations I have found (see the corresponding articles at the end of the post):

Investors price individual securities within an asset class the same (for example, large cap stocks or value stocks), instead of pricing the associated portfolio.

There exists higher demand for high volatility stocks. This is a consequence of an over-optimistic regarding high volatility stocks (hoping for high returns).

Portfolio managers mainly focus on tracking error, rather than total portfolio volatility.

Investors usually have leverage restrictions, and the good returns of low volatility investments cannot be easily arbitraged away.

Low volatility stocks are associated with a yet hidden risk factor, for instance similar to those proposed by Fama and French.

In a multi-period setting and over the long run, the average return of high volatility portfolios compounds slower than the return of low volatility ones.

Do you have any other explanation? I will be very pleased to add them to this post.

Finally, here is a selection of the literature I have read about this topic:

The last year annualized Sharpe ratio of the low vol strategy was 1.68 (after proportional transaction costs of 40 bps was discounted). On the other hand, the SR of the S&P 500 was 1.15 over the same period.

Finally, the correlation of the low vol strategy with the S&P 500 along the last 52 weeks was 84%.

Again, all these performance results are consistent over time.

This time, I am going to show you the excess return of the low vol portfolio (after transaction costs) respect to the S&P 500. The evolution is from 2006 up to now.

It can be observed that around 62% of the time, the low vol portfolio return is higher than that of the S&P 500. In contrast, the volatility of the low vol portfolio is always less than that of the S&P 500.

These results can be attained because the low vol portfolio does not present a large correlation with the market index. In the next graph, we show the evolution of the annualized tracking error (respect to the S&P 500) from 2006 up to now.

It can be observed that the mean tracking error is around 12%, relatively high. This allows for better expected returns.

As a summary, the low vol portfolio dominates the market index around 60% of the time in the risk-return space, showing they attain consistently better risk-adjusted returns.

The last year annualized Sharpe ratio of the low vol strategy was 0.62 (after proportional transaction costs of 40 bps was discounted). On the other hand, the SR of the IBEX 35 was 0.20 over the same period.

Finally, the correlation of the low vol strategy with the IBEX 35 along the last 52 weeks was 91%.

Again, all these performance results are consistent over time.

This time, I am going to show you the excess return of the low vol portfolio (after transaction costs) respect to the IBEX 35. The evolution is from 2009 up to now.

It can be observed that more than 80% of the time, the low vol portfolio return is higher than that of the IBEX 35. In contrast, the volatility of the low vol portfolio is always less than that of the IBEX 35.

These results can be attained because the low vol portfolio does not present a large correlation with the market index. In the next graph, we show the evolution of the annualized tracking error (respect to the IBEX 35) from 2009 up to now.

It can be observed that the mean tracking error is around 15%, relatively high. This allows for better expected returns.

As a summary, the low vol portfolio dominates the market index more than 80% of the time in the risk-return space, showing they attain consistently better risk-adjusted returns.